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Scintillations due to a concentrated layer with a power‐law turbulence spectrum
Author(s) -
Rumsey V. H.
Publication year - 1975
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs010i001p00107
Subject(s) - physics , intensity (physics) , turbulence , exponent , angular spectrum method , power law , spectral density , plane wave , spectrum (functional analysis) , plane (geometry) , computational physics , optics , mathematics , quantum mechanics , geometry , statistics , philosophy , linguistics , thermodynamics , diffraction
The spatial spectrum of intensity fluctuations due to a concentrated layer of turbulence is derived from the parabolic wave equation. The spectrum of refractive index fluctuations is taken to be an unmodified power law of arbitrary strength, with exponent α, 2 < α < 6. For 2 < α < 4 it is shown that the intensity spectra for a plane wave can be expressed in terms of a single parameter U , which is the Born approximation to m 2 , the normalized variance of intensity fluctuation. For U ≪ 1 the Born approximation applies. The high frequency approximation to the intensity spectrum is the angular spectrum that would result from twice the strength of turbulence. It applies above the spatial frequency κ f or 2π κ f / U , whichever is smaller, where κ f is the frequency at the first null of the Born approximation. For U > 30, it represents essentially all of the intensity fluctuations and shows that m saturates at unity for a plane wave as U → ∞. Simple formulas for m when the source has finite angular extent show that m decreases with increasing turbulence as U α−2 for U ≫ 1. These results are confirmed by exact calculations for the case α = 3 and by extensive observations of interplanetary scintillations.